As of August 2024, International Journal "Notes on Intuitionistic Fuzzy Sets" is being indexed in Scopus.
Please check our Instructions to Authors and send your manuscripts to nifs.journal@gmail.com. Next issue: September/October 2024.
Open Call for Papers: International Workshop on Intuitionistic Fuzzy Sets • 13 December 2024 • Banska Bystrica, Slovakia/ online (hybrid mode).
Deadline for submissions: 16 November 2024.

Issue:An outline for a new approach to clustering based on intuitionistic fuzzy relations

From Ifigenia, the wiki for intuitionistic fuzzy sets and generalized nets
(Redirected from Issue:Nifs/16/1/40-60)
Jump to navigation Jump to search
shortcut
http://ifigenia.org/wiki/issue:nifs/16/1/40-60
Title of paper: An outline for a new approach to clustering based on intuitionistic fuzzy relations
Author(s):
Dmitri Viattchenin
United Institute of Informatics Problems, National Academy of Sciences of Belarus, 6 Surganov Str. 220012 Minsk, Belarus
viattchenin@mail.ru
Published in: "Notes on Intuitionistic Fuzzy Sets", Volume 16 (2010) Number 1, pages 40—60
Download:  PDF (377  Kb, File info)
Abstract: The paper deals with the problem of clustering based on intuitionistic fuzzy relations. A heuristic method of possibilistic clustering is extended for of intuitionistic fuzzy tolerances. The extended clustering method is based on the concept of allotment among intuitionistic fuzzy clusters. The paper provides the description of basic ideas of the method of clustering. A plan of a direct clustering algorithm is described in detail. Illustrative examples of applications of the proposed algorithm to artificial data sets are given in comparison with the results of application of the Hung’s fuzzy clustering method. Preliminary conclusions are formulated and perspectives are outlined.


References:
  1. Atanassov K. Intuitionistic fuzzy sets // Fuzzy Sets and Systems. – 1986. – Vol. 20. – P. 87-96.
  2. Atanassov K. Intuitionistic Fuzzy Sets: Theory and Applications. – Heidelberg: Springer-Verlag, 1999.
  3. Bezdek J.C. Pattern Recognition with Fuzzy Objective Function Algorithms. – New York: Plenum Press, 1981.
  4. Burillo P., Bustince H. Intuitionistic fuzzy relations (Part I) // Mathware and Soft Computing. – 1995. – Vol. 2. – P. 5-38.
  5. Burillo P., Bustince H. Intuitionistic fuzzy relations (Part II). Effect of Atanassov’s operators on the properties of the intuitionistic fuzzy relations // Mathware and Soft Computing. – 1995. – Vol. 2. – P. 117-148.
  6. Hathaway R.J., Davenport J.W., Bezdek J.C. Relational duals of the C-means clustering algorithms // Pattern Recognition. – 1989. – Vol. 22. – P. 205-212.
  7. Höppner F., Klawonn F., Kruse R., Runkler T. Fuzzy Cluster Analysis: Methods for Classification, Data Analysis and Image Recognition. – Chichester: John Wiley & Sons, 1999.
  8. Hung W.-L., Lee J.-S., Fuh C.-D. Fuzzy clustering based on intuitionistic fuzzy relations // International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems. – 2004. – Vol. 12. – P. 513-529.
  9. Iakovidis D.K., Pelekis N., Kotsifakos E.E., Kopanakis I. Intuitionistic fuzzy clustering with applications in computer vision // Advanced Concepts for Intelligent Vision Systems: Proceedings of the 10th International Conference ACIVS’2008 (Juan-les-Pins, France, October 20-24, 2008) / J. Blanc-Talon, S. Bourennane, W. Philips, D. Popescu, P. Scheunders, eds. – Berlin: Springer-Verlag, 2008. – P. 764-774.
  10. Krishnapuram R., Keller J.M. A possibilistic approach to clustering // IEEE Transactions on Fuzzy Systems. – 1993. – Vol. 1. – P. 98-110.
  11. Pedrycz W. Conditional fuzzy C-means // Pattern Recognition Letters. – 1996. – Vol. 17. – P. 625-631.
  12. Pelekis N., Iakovidis D.K., Kotsifakos E.E., Kopanakis I. Fuzzy clustering of intuitionistic fuzzy data // International Journal of Business Intelligence and Data Mining. – 2008 – Vol. 3. – P. 45-65.
  13. Radecki T. Level fuzzy sets // Journal of Cybernetics. – 1977. – Vol. 7. – P. 189-198.
  14. Roubens M. Pattern classification problems and fuzzy sets // Fuzzy Sets and Systems. – 1978. – Vol. 1. – P. 239-253.
  15. Szmidt E., Kacprzyk J. Classification with nominal data using intuitionistic fuzzy sets // Foundations of Fuzzy Logic and Soft Computing: Proceedings of the 12th International Fuzzy Systems Association World Congress IFSA’2007 (Cancun, Mexico, June 18-21, 2007) / P. Melin, O. Castillo, L.T. Aguilar, J. Kacprzyk, W. Pedrycz, eds. – Berlin: Springer-Verlag, 2007. – P. 76-85.
  16. Torra V., Miyamoto S., Endo Y., Domingo-Ferrer J. On intuitionistic fuzzy clustering for its application to privacy // Proceedings of the 2008 IEEE World Congress on Computational Intelligence WCCI’2008 – 17th IEEE International Conference on Fuzzy Systems FUZZ-IEEE’08 (Hong Kong, China, June 1-6, 2008). – Piscataway: IEEE Press, 2008. – P. 1042-1048.
  17. Viattchenin D.A. A new heuristic algorithm of fuzzy clustering // Control & Cybernetics. – 2004. – Vol. 33. – P. 323-340.
  18. Viattchenin D.A. Parameters of the AFC–method of fuzzy clustering // Bulletin of The Military Academy of The Republic of Belarus. – 2004. – No. 4. – P. 51-55. (in Russian)
  19. Viattchenin D.A. Level fuzzy relations and their applications in pattern recognition // Bulletin of The Military Academy of The Republic of Belarus. – 2005. – No. 4. – P. 25-31. (in Russian)
  20. Viattchenin D.A. A direct algorithm of possibilistic clustering with partial supervision // Journal of Automation, Mobile Robotics and Intelligent Systems. – 2007. – Vol. 1, No. 3. – P. 29-38.
  21. Viattchenin D.A. On possibilistic interpretation of membership values in fuzzy clustering method based on the allotment concept // Proceedings of the Institute of Modern Knowledge. – 2008. – No. 3. – P. 85-90. (in Russian)
  22. Viattchenin D.A. Notes on the decomposition of intuitionistic fuzzy relations // Advances in Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets and Related Topics: Proceedings of the 7th International Workshop on Intuitionistic Fuzzy Sets and Generalized Nets IWIFSGN’2008 (Warsaw, Poland, October 17, 2008) / K.T. Atanassov, O. Hryniewicz, J. Kacprzyk, M. Krawczak, Z. Nahorski, E. Szmidt, S. Zadrozny, eds. – Warsaw: EXIT, 2008. – Vol. I: Foundations. – P. 251-262.
  23. Viattchenin D.A. An algorithm for detecting the principal allotment among fuzzy clusters and its application as a technique of reduction of analyzed features space dimensionality // Journal of Information and Organizational Sciences. – 2009. – Vol. 33, No. 1. – P. 205-217.
  24. Vlachos I.K., Sergiadis G.D. Intuitionistic fuzzy information – applications to pattern recognition // Pattern Recognition Letters. – 2006. – Vol. 28. – P. 197-206.
  25. Windham M.P. Numerical classification of proximity data with assignment measures // Journal of Classification. – 1985. – Vol. 2. – P. 157-172.
  26. Wu K.-L., Yang M.-S. Alternative C-means clustering algorithms // Pattern Recognition. – 2002. – Vol. 35. – P. 2267-2278.
  27. Xu Z., Chen J., Wu J. Clustering algorithm for intuitionistic fuzzy sets // Information Sciences. – 2008. – Vol. 178. – P. 3775-3790.
  28. Yang M.-S., Shih H.-M. Cluster analysis based on fuzzy relations // Fuzzy Sets and Systems. – 2001. – Vol. 120. – P. 197-212.
  29. Zimmermann H.-J. Fuzzy Set Theory and Its Applications. – Boston: Kluwer Academic Publishers, 1991.
Citations:

The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.

Retrieved from "https://ifigenia.org/index.php?title=Issue:An_outline_for_a_new_approach_to_clustering_based_on_intuitionistic_fuzzy_relations&oldid=12711"